CAT Probability Combinatorics Questions & Solutions
A sample of real CAT Probability Combinatorics past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 49 Probability Combinatorics questions in all — sign up free to practise them timed.
- Q1.CAT 2025
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is
880
840
800
600
- Q2.CAT 2022
The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is
2222
2442
2592
3333
- Q3.CAT 2021
A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is
Answer: 50
- Q4.CAT 2018
In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is
Answer: 1098
- Q5.CAT 2017
In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Answer: 6
Passage
Directions for the next two questions: The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
Q6.CAT 2008Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
[CAT 2008]
60
75
45
90
72
- Q7.CAT 2005
In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
200
216
235
256
- Q8.CAT 2004
In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
Lactose 0.16 Maltose 0.32 Glucose 0.74 Sucrose 1 Fructose 1.7 Saccharin 675 15
35
120
336
- Q9.CAT 2003
A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition
- Q10.CAT 2002
In how many ways is it possible to choose a white square and a black square on a chessboard so that the squares must not lie in the same row or column?
56
896
60
768
- Q11.CAT 2000
One red flag, three white flags and two blue flags are arranged in a line such that,
A. no two adjacent flags are of the same colour
B. the flags at the two ends of the line are of different colours.
In how many different ways can the flags be arranged?
6
4
10
2
- Q12.CAT 1997
In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a specific director?
9! × 2
2 × 8!
2 × 7!
None of these
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